This is a poor mans solution . . . and will only give you stereo, not full 6.1 sound . . . you can use a Monoprice 8-channel selector (see link below). Plug your front left/right speakers into the "in ports" of the 8-channel selector, then plug the other rooms set of speakers to 6 of the available "out port" zones/channels. You'll then have to connect the remaining two empty zones back to your speakers (so you'll end up using all eight zones, 6 for the other room, and two to output sound to your in room speakers) . . . then place your av receiver on 2, 6, or 7 channel stereo mode. If you keep all 8 zones turned on, you'll get sound in both rooms that way.
If you want to control the volume at the same time in both rooms, they also have an 8-channel channel selector with volume control (see link below).
Not a perfect solution, just an inexpensive one that will work in stereo mode.
I'm sure there are other expensive ways to accomplish true 6.1 sound in both room, but if your goal is just for music, which is primarily recorded in stereo mode anyway, will, this will work very inexpensively.
I use this one (does not have volume control), and for what it is, it works. No bells and whistles, but does exactly what the documentation says it will do:
This might work for you, too, has volume control, but you'll need to run both A/B lines on this device at the same time, which is possible (cost a little more):
Good luck . . . just note, this is just an inexpensive way . . . it won't break my heart if you need something "fancier".